Gravitational effects on light rays and binary pulsar energy loss in a scalar theory of gravity

TL;DR

This paper explores a scalar bimetric gravity theory with a preferred frame, deriving static solutions, post-Newtonian and post-Minkowskian approximations, and analyzing gravitational effects on light and binary pulsar energy loss.

Contribution

It introduces a scalar bimetric gravity framework with new static solutions and post-approximations, matching key predictions of general relativity for photons and gravitational radiation.

Findings

Reproduces Schwarzschild metric in static spherical case

No preferred-frame effect for photons at 1PN order

Binary system energy loss via quadrupole radiation matches Peters-Mathews coefficients

Abstract

A scalar bimetric theory of gravity with a preferred reference frame is summarized. Dynamics is governed by an extension of Newton's second law. In the static case, geodesic motion is recovered together with Newton's attraction field. In the static spherical case, Schwarzschild's metric is found. Asymptotic schemes of post-Newtonian (PN) and post-Minkowskian (PM) approximation are built, each based on associating a conceptual family of systems with the given system. At the 1PN approximation, there is no preferred-frame effect for photons, hence the standard predictions of GR for photons are got. At the 0PM approximation, an isolated system loses energy by quadrupole radiation, without any monopole or dipole term. Inserting this loss into the Newtonian 2-body problem gives the Peters-Mathews coefficients of the theory.